NCERT Solutions · Class 11 Chemistry Classification of Elements and Periodicity in Properties

The periodic table is organised so that elements with similar valence-shell electron configurations fall into the same column.The starting point is atomic number, not atomic mass. Every element is placed in order of increasing atomic number \(\displaystyle Z \) (the number of protons, which equals the number of electrons in a neutral atom). This ordering itself is not the "theme" — it is just the ruler. The real organising idea is what happens to the electron configuration as \(\displaystyle Z \) increases one at a time.As electrons are added one by one, they fill orbitals following the \(\displaystyle (n+l) \) rule (the Aufbau principle). Because orbitals of a given type (s, p, d, f) fill up in a repeating pattern — one s-subshell, then a set of p-subshells, and so on — the outermost (valence) electron configuration repeats at regular intervals of \(\displaystyle Z \). This repetition is the periodicity.Aside — this is the point most students skip past: the table is not arranged by mass, by size, or by "how the elements were discovered." It is arranged so that elements whose valence shells have the same configuration land directly beneath one another. For example, Li (configuration \(\displaystyle 1s^2\,2s^1 \)), Na (\(\displaystyle [\text{Ne}]\,3s^1 \)), and K (\(\displaystyle [\text{Ar}]\,4s^1 \)) all end in \(\displaystyle ns^1 \), so all three sit in Group $\displaystyle 1$, even though they differ enormously in mass and size.This gives the table its two directions of meaning: So the table is really a map of one underlying fact: chemical and physical properties of elements are a periodic function of their atomic numbers, because the arrangement of electrons in the outer shell — the part of the atom responsible for chemical behaviour — recurs periodically as \(\displaystyle Z \) increases. Grouping elements by matching valence configuration is what turns a simple numerical list ($\displaystyle 1$, $\displaystyle 2$, $\displaystyle 3$, $\displaystyle 4$, …) into a table with rows (periods) and columns (groups) that carry chemical meaning.Answer: Elements are arranged in order of increasing atomic number, in such a way that elements having similar valence-shell electronic configurations (and hence similar chemical properties) fall into the same vertical column (group), while a new principal shell begins with each row (period). This is the modern periodic law: properties of elements are a periodic function of their atomic number.

Mendeleev's classification used relative atomic mass — but the properties of the elements always won when the two disagreed.The property he usedMendeleev arranged the (then) $\displaystyle 63$ known elements in order of increasing atomic mass, and stated what is now called Mendeleev's Periodic Law:"The physical and chemical properties of elements are a periodic function of their atomic masses."In practice this meant: list the elements in a row by rising atomic mass, and when an element's chemical and physical behaviour (valency, oxide/hydride formula, general reactivity) started repeating an earlier element's behaviour, start a new row directly under it. The column that results (a "group") collects elements with similar properties, because atomic mass, arranged this way, tracked periodicity closely enough for the elements known at the time.Did he stick to it? No — not strictly.Mendeleev treated similarity of chemical properties as the higher authority, and atomic mass as the ordering rule only as long as it did not contradict that. In a small number of places the two clashed, and he broke the atomic-mass order to keep chemically similar elements together. Two classic examples: He also left gaps in the table (for elements not yet discovered, such as eka-aluminium and eka-silicon, later identified as gallium and germanium) rather than force the known elements to fill every atomic-mass slot — a further sign that the organizing principle in his mind was recurring properties, with atomic mass serving as a convenient but not absolute ordering tool.This is exactly the flaw atomic mass carried: it does not correlate perfectly with chemical behaviour across all elements, which is why the modern periodic law later replaced it with atomic number (Moseley), removing the need for any such exceptions.Answer: Mendeleev classified elements by increasing relative atomic mass (his Periodic Law: properties are a periodic function of atomic mass). He did not stick to this strictly — wherever atomic-mass order conflicted with the elements' actual chemical properties, he reordered elements to keep similar properties together (e.g., cobalt before nickel, tellurium before iodine, despite their higher atomic mass), and left gaps for undiscovered elements rather than force a fit.

Mendeleev's Law used atomic mass; the Modern Periodic Law uses atomic number — and that swap is what fixed the periodic table.Mendeleev's Periodic Law states that the physical and chemical properties of elements are a periodic function of their atomic masses. Mendeleev arranged all known elements in order of increasing atomic mass, and found that elements with similar properties recurred at regular intervals.The Modern Periodic Law states that the physical and chemical properties of elements are a periodic function of their atomic numbers, where the atomic number \(\displaystyle Z \) is the number of protons in the nucleus of an atom (and, for a neutral atom, also the number of electrons).So the basic difference in approach is the ordering variable itself: mass versus atomic number. This is not a small technical swap — it changes why periodicity happens at all. **Answer: Mendeleev's Periodic Law orders elements by atomic mass, while the Modern Periodic Law orders them by atomic number. Since atomic number equals the number of protons/electrons and directly fixes the valence electronic configuration, the modern approach ties periodicity to its actual physical cause and removes the anomalies (such as the Co–Ni and Te–I misplacements, and the problem of isotopes) that atomic-mass ordering could not explain.

A period's length is fixed by which orbitals actually get filled while the \(\displaystyle (n+l)\) rule is obeyed — not by the total capacity of one shell. The natural mistake here is to say "period $\displaystyle 6$ means \(\displaystyle n=6\), so the answer is \(\displaystyle 2n^2 = 72\)." That formula gives the total electron capacity of an entire isolated shell, but a period is not "one shell filling up" — it is a stretch of the actual, energy-ordered filling sequence, and for \(\displaystyle n=6\) that sequence pulls in orbitals from \(\displaystyle n=4\) and \(\displaystyle n=5\) as well.Step $\displaystyle 1$ — what the four quantum numbers say about a subshell's capacity. So the maximum number of electrons a subshell of azimuthal number \(\displaystyle l\) can hold is \[N_{\max} = 2(2l+1) \] where the factor \(\displaystyle 2\) comes from the two spin states and \(\displaystyle (2l+1)\) from the number of orbitals. This gives: \[\text{s: } 2(1)=2,\qquad \text{p: } 2(3)=6,\qquad \text{d: } 2(5)=10,\qquad \text{f: } 2(7)=14 . \]Step $\displaystyle 2$ — which subshells actually belong to period 6.Orbitals do not fill in the naive order 6s, 6p, 6d, 6f, …; they fill in order of increasing \(\displaystyle (n+l)\), and for equal \(\displaystyle (n+l)\) the orbital with the lower \(\displaystyle n\) goes first (Aufbau's \(\displaystyle (n+l)\) rule). Working through the sequence — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, … — shows that once 6s has been reached, the next three subshells to fill, before 7s begins, are 4f, 5d, and 6p, not 6d or 6f. That interleaving of a lower-\(\displaystyle n\), higher-\(\displaystyle l\) orbital (4f) among the \(\displaystyle n=6\) orbitals is exactly why the \(\displaystyle 2n^2\) shortcut fails here.Step $\displaystyle 3$ — add up the capacities of 6s, 4f, 5d, 6p.\[\underbrace{2}_{6s} + \underbrace{14}_{4f} + \underbrace{10}_{5d} + \underbrace{6}_{6p} = 32 . \]Step $\displaystyle 4$ — check this against the actual period. Period $\displaystyle 6$ runs from caesium (\(\displaystyle Z=55\)) to radon (\(\displaystyle Z=86\)): \[86 - 55 + 1 = 32, \] which is the same number, and it is built from exactly this filling: Cs, Ba fill 6s ($\displaystyle 2$ elements); Ce to Lu fill 4f, the lanthanides ($\displaystyle 14$ elements); La/Lu through Hg fill 5d ($\displaystyle 10$ elements); Tl to Rn fill 6p ($\displaystyle 6$ elements).So the $\displaystyle 32$ elements of period $\displaystyle 6$ are accounted for, orbital by orbital, by the quantum-number capacities of 6s, 4f, 5d and 6p — not by treating \(\displaystyle n=6\) as a single shell filling from empty to \(\displaystyle 2n^2=72\).Answer: Period $\displaystyle 6$ has $\displaystyle 32$ elements because the orbitals that fill during this period, in the order fixed by the \(\displaystyle (n+l)\) rule, are 6s, 4f, 5d and 6p, whose quantum-number-determined capacities are $\displaystyle 2$, $\displaystyle 14$, $\displaystyle 10$ and $\displaystyle 6$ electrons respectively; \(\displaystyle 2+14+10+6 = 32\), matching the $\displaystyle 32$ elements from caesium (Z = $\displaystyle 55$) to radon (Z = $\displaystyle 86$).

The period number is the highest principal quantum number \(\displaystyle n\) reached while filling electrons; the group number (for a p-block element) is found from how many electrons sit in the outermost \(\displaystyle ns\) and \(\displaystyle np\) subshells.Build up the electron configuration of \(\displaystyle Z = 114\) by the Aufbau order, filling one subshell at a time and keeping a running total of electrons so nothing is skipped:\[1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^{10}\,4p^6\,5s^2\,4d^{10}\,5p^6\,6s^2\,4f^{14}\,5d^{10}\,6p^6\,7s^2\,5f^{14}\,6d^{10}\,7p^2 \]Here each symbol \(\displaystyle n\ell^{x}\) means: \(\displaystyle n\) is the shell (principal quantum number), \(\displaystyle \ell\) is the subshell type (\(\displaystyle s,p,d,f\)), and the superscript \(\displaystyle x\) is the number of electrons sitting in that subshell.Running total of electrons as each subshell fills:\[2,\,4,\,10,\,12,\,18,\,20,\,30,\,36,\,38,\,48,\,54,\,56,\,70,\,80,\,86,\,88,\,102,\,112,\,114 \]The total reaches exactly $\displaystyle 114$ after the \(\displaystyle 7p^2\) subshell is filled, so no electron is left over and none is missing — the configuration is confirmed:\[[\text{Rn}]\,5f^{14}\,6d^{10}\,7s^2\,7p^2 \](A common slip here is to stop counting once the numbers "look big enough" and guess the period from the noble-gas symbol alone — \(\displaystyle [\text{Rn}]\) is only the core; you still have to add up the outer $\displaystyle 28$ electrons to see that the last electron actually lands in the \(\displaystyle 7p\) subshell, not the \(\displaystyle 6d\) or \(\displaystyle 5f\).)Finding the period. The outermost shell being filled is \(\displaystyle n = 7\) (the \(\displaystyle 7s\) and \(\displaystyle 7p\) electrons), so the element sits in Period $\displaystyle 7$.Finding the group. The element's last electron enters a \(\displaystyle p\) subshell, so it is a p-block element. For p-block elements, the group number is obtained from the number of electrons in the outermost \(\displaystyle ns\) and \(\displaystyle np\) subshells by\[\text{Group number} = 10 + (\text{electrons in } ns) + (\text{electrons in } np) \]Here the valence configuration is \(\displaystyle 7s^2\,7p^2\), so electrons in \(\displaystyle ns\) = $\displaystyle 2$ and electrons in \(\displaystyle np\) = $\displaystyle 2$:\[\text{Group number} = 10 + 2 + 2 = 14 \]This is exactly the pattern of the carbon family: carbon (\(\displaystyle 2s^2 2p^2\)), silicon (\(\displaystyle 3s^2 3p^2\)), germanium (\(\displaystyle 4s^2 4p^2\)), tin (\(\displaystyle 5s^2 5p^2\)), and lead (\(\displaystyle 6s^2 6p^2\)) all end in \(\displaystyle ns^2np^2\) and all sit in Group $\displaystyle 14$ — \(\displaystyle Z = 114\) simply continues that column one row further down, directly below lead.Answer: The element with \(\displaystyle Z = 114\) has the configuration \(\displaystyle [\text{Rn}]\,5f^{14}6d^{10}7s^27p^2\), so it belongs to Period $\displaystyle 7$ and Group $\displaystyle 14$ (the carbon family), directly below lead.

An element's address in the periodic table — (period, group) — fixes its electron configuration uniquely, and the configuration fixes the atomic number. Two rules link the address to the configuration:1. The period number equals \(\displaystyle n\), the principal quantum number of the outermost (valence) shell being filled. Period $\displaystyle 3$ means the valence electrons sit in the \(\displaystyle n=3\) shell. 2. For the p-block (Groups $\displaystyle 13$–$\displaystyle 18$), the group number equals \(\displaystyle 10 +\) (number of valence electrons). This is a direct reading of the IUPAC $\displaystyle 1$–$\displaystyle 18$ group labels: Group $\displaystyle 13$ has $\displaystyle 3$ valence electrons, Group $\displaystyle 14$ has $\displaystyle 4$, …, Group $\displaystyle 18$ has 8.A common slip here is to treat "third period" as if it meant atomic number $\displaystyle 3$ (that would be lithium, which is actually in period $\displaystyle 2$) — period number and atomic number are not the same thing; the period only tells you which shell is being filled, not how many electrons are in it.Step $\displaystyle 1$ — find the number of valence electrons. Group $\displaystyle 17$ is a p-block group, so \[\text{valence electrons} = 17 - 10 = 7 \]Step $\displaystyle 2$ — write the valence-shell configuration. With \(\displaystyle n = 3\) (period $\displaystyle 3$) and $\displaystyle 7$ valence electrons distributed as \(\displaystyle ns^2np^5\) ($\displaystyle 2$ in the s-subshell, the remaining $\displaystyle 5$ in the p-subshell): \[3s^2\,3p^5 \]Step $\displaystyle 3$ — build the full electron configuration. The shells below \(\displaystyle n=3\) are completely filled, following the order \(\displaystyle 1s,\,2s,\,2p\) before \(\displaystyle 3s,\,3p\): \[1s^2\,2s^2\,2p^6\,3s^2\,3p^5 \]Step $\displaystyle 4$ — count the electrons to get the atomic number. \[2 + 2 + 6 + 2 + 5 = 17 \] For a neutral atom, the number of electrons equals the number of protons, and the number of protons is the atomic number \(\displaystyle Z\). So \(\displaystyle Z = 17\).Cross-check by walking the row of the table. Period $\displaystyle 3$ runs Na($\displaystyle 11$), Mg($\displaystyle 12$), Al($\displaystyle 13$), Si($\displaystyle 14$), P($\displaystyle 15$), S($\displaystyle 16$), Cl($\displaystyle 17$), Ar($\displaystyle 18$) — there is no d-block in period $\displaystyle 3$ (the d-block only begins at period $\displaystyle 4$), so Group $\displaystyle 13$ lands immediately after Group 2. Counting across, Group $\displaystyle 17$ in this row is Cl, with atomic number $\displaystyle 17$ — the same answer as the configuration method. This element is chlorine, a halogen, consistent with Group $\displaystyle 17$ elements always having the \(\displaystyle ns^2np^5\) valence pattern that makes them one electron short of a full octet.Answer: The element in the third period and seventeenth group is chlorine (Cl), atomic number $\displaystyle 17$ (electron configuration \(\displaystyle 1s^2\,2s^2\,2p^6\,3s^2\,3p^5\)).

A new element's name almost always tells you who fought to get credit for finding it — read the naming dispute the chapter itself describes, and match each group to the element whose story is theirs.This question sits right after the NCERT passage on nomenclature of elements with atomic number greater than $\displaystyle 100$ (Section $\displaystyle 3.4$). Two separate pieces of that passage answer the two parts.(i) Lawrence Berkeley LaboratoryThe text says: "both American and Soviet scientists claimed credit for discovering element 104. The Americans named it Rutherfordium whereas Soviets named it Kurchatovium."The American team in that priority dispute worked at the Lawrence Berkeley Laboratory in California — this is the lab that raced the Dubna (USSR) group to synthesise element with atomic number \(\displaystyle Z = 104 \) and proposed the name Rutherfordium (Rf), after the nuclear physicist Ernest Rutherford. So Lawrence Berkeley Laboratory is the group behind the name Rutherfordium.A point students often miss here: the element is not named after Berkeley or after anyone at the lab — Rutherfordium honours Rutherford, a scientist with no connection to the lab itself. The lab's role was only in the discovery and naming claim, not in whose name got used.(ii) Seaborg's groupThe chapter's own footnote on Glenn T. Seaborg says: "Glenn T. Seaborg's work... starting with the discovery of plutonium in $\displaystyle 1940$, followed by those of all the transuranium elements from $\displaystyle 94$ to $\displaystyle 102$ led to reconfiguration of the periodic table... In $\displaystyle 1951$, Seaborg was awarded the Nobel Prize in chemistry for his work. Element $\displaystyle 106$ has been named Seaborgium (Sg) in his honour."Seaborg's group is the specific research team, built around Glenn Seaborg himself, that had already discovered plutonium and the run of transuranium elements up to \(\displaystyle Z = 102 \). When this same team went on to synthesise the element with atomic number \(\displaystyle Z = 106 \), it named the element after its own leader — giving Seaborgium (Sg).Here is the distinction the question is testing: "Lawrence Berkeley Laboratory" names an institution involved in a priority dispute over element $\displaystyle 104$, while "Seaborg's group" names a specific team, tied to one scientist's own body of work, that discovered and named element $\displaystyle 106$ after him.Answer: (i) Lawrence Berkeley Laboratory would have named the element with atomic number $\displaystyle 104$ as Rutherfordium (Rf), after Ernest Rutherford. (ii) Seaborg's group would have named the element with atomic number $\displaystyle 106$ as Seaborgium (Sg), in honour of Glenn T. Seaborg himself.

Elements placed in the same group have the same number of electrons in their outermost (valence) shell — and it is this valence-shell configuration, not the atomic number itself, that decides how an element behaves.The modern periodic law states that properties of elements are a periodic function of their atomic number. Electrons fill orbitals in a repeating pattern: within every period the outer shell fills up in the same order — \[ns^1,\ ns^2,\ ns^2np^1,\ ns^2np^2,\ \ldots,\ ns^2np^6 \] — only the value of the principal quantum number \(\displaystyle n\) (the shell number) increases as you drop to the next period. A group is simply the column you get by lining up elements that sit at the same stage of this repeating pattern, so every member of a group has an analogous valence-shell configuration, just written for a different \(\displaystyle n\).Why this makes chemical properties similarChemical behaviour — the valency an element shows, the type of ion it forms, the kind of bonds it makes, its characteristic reactions — is controlled almost entirely by the number and arrangement of valence electrons, because these are the electrons available to be lost, gained, or shared. Since every element in a group has the same valence-electron count, they behave in the same type of way: This is the point students most often blur: a shared group does not mean identical properties, only the same pattern of chemical behaviour, because the number of valence electrons — the thing chemistry actually reacts with — is what repeats, not the whole atom.Why physical properties follow a family trend tooPhysical properties (atomic radius, ionisation enthalpy, electronegativity, metallic character) also vary as a regular, predictable trend down a group rather than randomly, because going down a group the valence-electron count stays fixed while the principal quantum number \(\displaystyle n\) increases by one every period — a new shell of electron density is added each time. This steadily increases the distance of the valence electrons from the nucleus, so radius increases smoothly, ionisation enthalpy decreases smoothly, and so on. It is this steady, non-erratic change that gives a group its "family resemblance" — soft, low-melting alkali metals; coloured, corrosive halogens — even though the exact numerical value of a property (say, the melting point) is different for each member.Answer: Elements in the same group have the same number of valence electrons and an analogous valence-shell electronic configuration (only the principal quantum number \(\displaystyle n\) differs), and it is this valence-shell configuration that fixes chemical behaviour (valency, ions formed, bond type, characteristic reactions) — so group members react in the same characteristic way. Physical properties also change in a smooth, regular trend down the group (not identically, but systematically) because the number of occupied shells increases steadily while the valence-electron count stays constant, steadily changing atomic size and how tightly the valence electrons are held.

Neither radius is the edge of a solid little ball — an atom's electron cloud has no sharp boundary, so both radii are distances measured between nuclei and then split by convention.Quantum mechanically, the probability of finding an electron never drops to exactly zero, however far you go from the nucleus — the electron density just fades out, trailing off toward infinity. There is no point you can point to and say "the atom ends here." So chemists do not measure a single isolated atom's radius directly; instead they measure the distance between the nuclei of two neighbouring atoms (from X-ray or electron diffraction) and take a fraction of that distance as "the radius." That is what atomic radius really is: an operational, not an absolute, quantity, and its value even changes depending on how the neighbouring atom is bonded.Atomic radius: half the internuclear distance, and it comes in three flavours depending on the kind of contact The aside worth remembering here: these three numbers for the same element are all different, because "radius" is really answering the question "how close can this atom get to a neighbour under this particular kind of contact," not "how big is this atom in isolation."Ionic radius: the same trick, applied to an ionic crystal, then apportioned between the two ionsFor an ionic solid, X-ray diffraction gives the distance between the nucleus of the cation and the nucleus of the adjacent anion in the lattice — this is \(\displaystyle r_{+} + r_{-} \), the sum of the two ionic radii, not either one alone. To split this sum into an individual cation radius and anion radius, one ion's radius must be fixed independently (for instance, from a series of compounds where that ion's size can be cross-checked), and the rest is obtained by subtraction. So an individual ionic radius, too, is a value assigned by convention against a reference, not a directly observed single-ion measurement.Why a cation is smaller, and an anion is larger, than the parent atom A related pattern worth flagging as the step people mix up: for an isoelectronic series (ions/atoms with the same number of electrons, e.g., \(\displaystyle \text{O}^{2-}, \text{F}^{-}, \text{Na}^{+}, \text{Mg}^{2+}, \text{Al}^{3+} \), all with $\displaystyle 10$ electrons), the number of electrons is fixed, so radius is governed entirely by nuclear charge: more protons pull the same electron cloud in tighter, so radius decreases as atomic number increases across the series — \(\displaystyle \text{O}^{2-} > \text{F}^{-} > \text{Na}^{+} > \text{Mg}^{2+} > \text{Al}^{3+} \).**Answer: Atomic radius is the distance from an atom's nucleus to the outermost shell where its electron density effectively ends — but since the electron cloud has no sharp edge, it is in practice defined and measured as half the distance between the nuclei of two touching neighbouring atoms (covalent radius for bonded atoms, van der Waals radius for non-bonded touching atoms, metallic radius for atoms in a metal lattice). Ionic radius is the same idea applied to an ion in a crystal: the interionic (nucleus-to-nucleus) distance between a cation and an adjacent anion is measured, and then split between the two using one ion's independently known radius as reference. A cation is smaller than its parent atom (fewer electrons, often a lost shell, higher effective nuclear charge per electron), while an anion is larger than its parent atom (more electrons, greater repulsion, lower effective nuclear charge per electron).

Atomic radius is set by a tug-of-war between the pull of the nucleus and the number of electron shells around it — and moving across a period changes one side of that fight, while moving down a group changes the other.Definition first. Atomic radius is usually measured as the covalent radius — half the distance between the nuclei of two like atoms joined by a single covalent bond (for metals, the metallic radius; for noble gases, the van der Waals radius, which is defined differently and is discussed below). The pull an outer electron actually feels is the effective nuclear charge \(\displaystyle Z_{eff} \), given by\[Z_{eff} = Z - \sigma \]where \(\displaystyle Z \) is the atomic number (the actual number of protons in the nucleus) and \(\displaystyle \sigma \) is the screening (shielding) constant — the extent to which the inner electrons block the full pull of the nucleus from reaching an outer electron. A bigger \(\displaystyle Z_{eff} \) pulls the outer electron in tighter, shrinking the atom; a smaller \(\displaystyle Z_{eff} \) lets it sit farther out.Across a period (left to right): atomic radius decreases.Moving one element to the next across a period, one proton is added to the nucleus (\(\displaystyle Z \) increases by $\displaystyle 1$) and one electron is added to the same principal shell (the same value of \(\displaystyle n \)) that was already being filled. Electrons in the same shell shield each other very poorly — the screening constant \(\displaystyle \sigma \) rises only a little for each added electron. So \(\displaystyle Z_{eff} = Z - \sigma \) goes up steadily across the period. The nucleus pulls the whole electron cloud in harder with each step, and the atomic radius shrinks.For example, across period $\displaystyle 2$ the covalent radii (in pm) fall steadily:\[\text{Li (152)} > \text{Be (111)} > \text{B (88)} > \text{C (77)} > \text{N (74)} > \text{O (66)} > \text{F (64)} \]The place this trips people up: the noble gas at the very end of the period (Ne, Ar, …) is usually tabulated with a larger radius than the halogen before it, which looks like it breaks the trend. It doesn't, because it isn't measured the same way — a noble gas forms no covalent bond, so its size has to be reported as a van der Waals radius (half the distance between two non-bonded atoms just touching each other), which is always larger than a covalent radius for a comparable atom. Comparing a van der Waals radius to a covalent radius is comparing two different rulers, so this last point is excluded when the period trend is stated.Down a group (top to bottom): atomic radius increases.Moving down a group, the outermost electron is no longer added to the same shell — a whole new principal shell is added, so \(\displaystyle n \) increases by $\displaystyle 1$ at every step. Nuclear charge \(\displaystyle Z \) does increase too, but now every electron in all the complete inner shells lies between the nucleus and the new outer electron, and a complete inner shell screens much more effectively than same-shell electrons do. The extra shielding from these full inner shells largely cancels the extra nuclear charge, so \(\displaystyle Z_{eff} \) on the valence electron stays roughly the same (or rises only slightly) down a group. What dominates instead is simply that the valence electron now occupies a shell of higher \(\displaystyle n \), which by itself sits farther from the nucleus. The result is a steady increase in atomic radius.For example, down group $\displaystyle 1$, the covalent radii (in pm) rise steadily:\[\text{Li (152)} < \text{Na (186)} < \text{K (231)} < \text{Rb (244)} < \text{Cs (262)} \]Answer: Atomic radius decreases across a period from left to right, because electrons added within the same shell shield each other poorly, so the effective nuclear charge \(\displaystyle Z_{eff}=Z-\sigma \) rises and pulls the electron cloud in tighter. Atomic radius increases down a group from top to bottom, because a new principal shell (higher \(\displaystyle n \)) is added at each step, and the extra shielding from the newly complete inner shells largely offsets the increased nuclear charge, so the dominant effect is simply that the valence electrons now occupy a shell farther from the nucleus.